Analyse Factorielle Multiple (AFM) avec FactoMineR sur la

Analyse Factorielle Multiple (AFM) avec FactoMineRsur la description sensorielle de vins

Fran?ois Husson

Chargement de FactoMineR

library(FactoMineR)data(wine)

L’AFM

res <- MFA(wine, group=c(2,5,3,10,9,2), type=c("n",rep("s",5)),ncp=5, name.group=c("orig","olf","vis","olfag","gust","ens"),num.group.sup=c(1,6))

1

−4 −2 0 2 4

02

46

Individual factor map

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

Saumur

BourgueuilChinon

ReferenceEnv1

Env2

Env4

olfvisolfaggust

!!!!!# R?sum? des r?sultats On peut obtenir un r?sum? des principaux r?sultats en utilisant la fonction summary.

summary(res)

Nous demandons ici ? avoir les r?sultats sur les 2 premi?res dimensions pour ?viter d’avoir des tableaux tropgrands (par d?faut, la fonction retourne les r?sultats des 3 premi?res dimensions).

summary(res, ncp=2)

#### Call:## MFA(base = wine, group = c(2, 5, 3, 10, 9, 2), type = c("n",## rep("s", 5)), ncp = 5, name.group = c("orig", "olf", "vis",## "olfag", "gust", "ens"), num.group.sup = c(1, 6))###### Eigenvalues

2

## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6## Variance 3.462 1.367 0.615 0.372 0.270 0.202## % of var. 49.378 19.494 8.778 5.309 3.857 2.887## Cumulative % of var. 49.378 68.873 77.651 82.960 86.816 89.703## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11 Dim.12## Variance 0.176 0.126 0.105 0.079 0.074 0.060## % of var. 2.506 1.796 1.502 1.124 1.054 0.861## Cumulative % of var. 92.209 94.005 95.506 96.630 97.684 98.545## Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18## Variance 0.029 0.022 0.019 0.011 0.009 0.006## % of var. 0.409 0.313 0.273 0.156 0.131 0.091## Cumulative % of var. 98.954 99.268 99.541 99.697 99.827 99.918## Dim.19 Dim.20## Variance 0.003 0.002## % of var. 0.047 0.035## Cumulative % of var. 99.965 100.000#### Groups## Dim.1 ctr cos2 Dim.2 ctr## olf | 0.782 22.591 0.380 | 0.620 45.346## vis | 0.855 24.688 0.728 | 0.040 2.937## olfag | 0.925 26.712 0.625 | 0.469 34.309## gust | 0.900 26.009 0.722 | 0.238 17.408## cos2## olf 0.239 |## vis 0.002 |## olfag 0.161 |## gust 0.050 |#### Supplementary groups## Dim.1 cos2 Dim.2 cos2## orig | 0.296 0.033 | 0.643 0.156 |## ens | 0.619 0.380 | 0.254 0.064 |#### Individuals (the 10 first)## Dim.1 ctr cos2 Dim.2 ctr## 2EL | 0.239 0.078 0.009 | -0.797 2.211## 1CHA | -2.045 5.751 0.257 | -1.383 6.667## 1FON | -1.220 2.048 0.187 | -0.459 0.734## 1VAU | -4.381 26.404 0.426 | 0.995 3.446## 1DAM | 2.696 9.996 0.462 | -0.120 0.050## 2BOU | 0.869 1.038 0.116 | -0.326 0.371## 1BOI | 1.553 3.318 0.294 | -0.280 0.272## 3EL | 0.129 0.023 0.001 | 0.789 2.167## DOM1 | -0.066 0.006 0.001 | -0.253 0.222## 1TUR | -1.202 1.987 0.184 | -0.375 0.489## cos2## 2EL 0.098 |## 1CHA 0.118 |## 1FON 0.026 |## 1VAU 0.022 |## 1DAM 0.001 |## 2BOU 0.016 |## 1BOI 0.010 |

3

## 3EL 0.052 |## DOM1 0.017 |## 1TUR 0.018 |#### Continuous variables (the 10 first)## Dim.1 ctr cos2 Dim.2 ctr## Odor.Intensity.before.shaking | 0.591 4.497 0.349 | 0.667 14.530## Aroma.quality.before.shaking | 0.835 8.989 0.698 | -0.075 0.186## Fruity.before.shaking | 0.716 6.606 0.513 | -0.151 0.741## Flower.before.shaking | 0.439 2.480 0.192 | -0.409 5.469## Spice.before.shaking | 0.038 0.019 0.001 | 0.865 24.420## Visual.intensity | 0.881 7.912 0.776 | 0.238 1.466## Nuance | 0.862 7.577 0.744 | 0.234 1.408## Surface.feeling | 0.950 9.198 0.903 | 0.049 0.063## Odor.Intensity | 0.627 2.416 0.393 | 0.576 5.155## Quality.of.odour | 0.791 3.844 0.626 | -0.410 2.612## cos2## Odor.Intensity.before.shaking 0.445 |## Aroma.quality.before.shaking 0.006 |## Fruity.before.shaking 0.023 |## Flower.before.shaking 0.168 |## Spice.before.shaking 0.748 |## Visual.intensity 0.057 |## Nuance 0.055 |## Surface.feeling 0.002 |## Odor.Intensity 0.331 |## Quality.of.odour 0.168 |#### Supplementary continuous variables## Dim.1 cos2 Dim.2 cos2## Overall.quality | 0.747 0.558 | -0.504 0.254 |## Typical | 0.766 0.586 | -0.466 0.217 |#### Supplementary categories## Dim.1 cos2 v.test Dim.2 cos2## Saumur | 0.533 0.483 1.343 | 0.350 0.209## Bourgueuil | -0.392 0.176 -0.596 | -0.504 0.291## Chinon | -0.877 0.537 -1.022 | -0.207 0.030## Reference | 1.437 0.823 2.442 | -0.567 0.128## Env1 | -0.949 0.614 -1.613 | -0.467 0.149## Env2 | -0.794 0.554 -1.067 | 0.191 0.032## Env4 | 0.277 0.008 0.216 | 3.141 0.971## v.test## Saumur 1.405 |## Bourgueuil -1.219 |## Chinon -0.384 |## Reference -1.534 |## Env1 -1.263 |## Env2 0.409 |## Env4 3.899 |

4

Graphe des individus et des modalit?s

plot(res)

−4 −2 0 2

−2

−1

01

23

4


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

2EL

1CHA

1FON

1VAU

1DAM

2BOU1BOI

3EL

DOM11TUR

4EL PER1

2DAM1POY

1ING

1BEN2BEA

1ROC2ING

T1

T2

Saumur

Bourgueuil

ChinonReferenceEnv1

Env2

Env4

plot(res, invisible="quali")

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−2

−1

01

23

4Individual factor map

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

2EL

1CHA

1FON

1VAU

1DAM2BOU

1BOI

3EL

DOM11TUR

4EL PER1

2DAM1POY1ING

1BEN2BEA

1ROC2ING

T1

T2

plot(res, invisible="quali", cex=0.8)

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−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

2EL

1CHA

1FON

1VAU

1DAM2BOU 1BOI

3EL

DOM11TUR

4EL PER1

2DAM

1POY1ING1BEN

2BEA

1ROC2ING

T1

T2

plot(res, invisible="quali", cex=0.8, partial=c("1VAU","PER1"))

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−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

2EL

1CHA

1FON

1VAU

1DAM2BOU 1BOI

3EL

DOM11TUR

4EL PER1

2DAM

1POY1ING1BEN

2BEA

1ROC

2ING

T1

T2

olfvisolfaggust

# Graphe des individus avec s?lection

plot(res, invisible="quali", cex=0.8, partial=c("1VAU","PER1"), select="cos2 0.4")

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−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2DAM2ING

T1

T2

olfvisolfaggust

plot(res, ,invisible="quali", partial="all",palette=palette(c("black","transparent","transparent","blue","transparent")))

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−8 −6 −4 −2 0 2 4 6

−4

−2

02

46


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

2EL 1CHA

1FON

1VAU

1DAM2BOU1BOI

3EL

DOM11TUR

4EL PER1

2DAM1POY1ING

1BEN2BEA

1ROC2ING

T1

T2

olfag

plot(res, invisible="quali", habillage=1, cex=0.8, select="cos2 0.4")

10

−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2DAM2ING

T1

T2

SaumurBourgueuilChinon

plot(res, invisible="quali", habillage="Soil", cex=0.8, select="cos2 0.4")

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−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2DAM2ING

T1

T2

ReferenceEnv1Env2Env4

plot(res, invisible="quali", habillage="Soil", cex=0.8, select="contrib 5")

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−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2ING

T1

T2


plot(res, invisible="quali", habillage="Soil", cex=0.8, select="contrib 5", unselect=0)

13

−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2ING

T1

T2


plot(res, invisible="quali", habillage="Soil", cex=0.8, select="contrib 5", unselect=1)

14

−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2ING

T1

T2


plot(res, invisible="quali", habillage="Soil", cex=0.8, select="contrib 5", unselect="grey70")

15

−4 −2 0 2

−2

−1

01

23


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

1VAU

1DAM

2ING

T1

T2


plot(res, invisible="quali", habillage="Soil", cex=0.8, select="contrib 5",unselect="grey70", axes=3:4)

16

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

−1.

5−

1.0

−0.

50.

00.

51.


Dim 3 (8.78%)

Dim

4 (

5.31

%)

1CHA

2BOU

3EL

2BEA

T1


plot(res, invisible="quali", habillage="Soil", cex=0.8, select=c("1VAU","PER1"),unselect="grey70", axes=3:4)

17

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

−1.

5−

1.0

−0.

50.

00.

51.


Dim 3 (8.78%)

Dim

4 (

5.31

%) 1VAU

PER1


# Graphe des variables

plot(res, choix="var")

18

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

−1.

0−

0.5

0.0

0.5

1.0

Correlation circle

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

olfvisolfaggustens Odor.Intensity.before.shaking

Aroma.quality.before.shakingFruity.before.shaking

Flower.before.shaking

Spice.before.shaking

Visual.intensityNuance

Surface.feeling

Odor.Intensity

Quality.of.odourFruity

Flower

SpicePlante

Phenolic

Aroma.intensity

Aroma.persistency

Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony

Overall.qualityTypical

plot(res, choix="var", shadow=TRUE)

19

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

−1.

0−

0.5

0.0

0.5

1.0

Correlation circle

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

olfvisolfaggustens Odor.Intensity.before.shaking





Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic

Aroma.intensityAroma.persistency

Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony

Overall.quality Typical

Odor.Intensity.before.shaking





Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony







Surface.feeling

Odor.Intensity


Flower

SpicePlante

Phenolic


Aroma.quality

Attack.intensity

AcidityAstringency

Alcohol

BalanceSmooth

Bitterness

Intensity

Harmony


plot(res, choix="var", shadow=TRUE, select="contrib 5")

20

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

−1.

0−

0.5

0.0

0.5

1.0

Correlation circle

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

olfvisolfaggustens


Aroma.quality.before.shaking


Visual.intensitySurface.feeling

































plot(res, choix="var", shadow=TRUE, select="contrib 5", axes=3:4)

21

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

−1.

0−

0.5

0.0

0.5

1.0

Correlation circle

Dim 3 (8.78%)

Dim

4 (

5.31

%)

olfvisolfaggustens


Fruity.before.shaking


FruityFlowerAroma.quality.before.shaking
























FruityFlower

# Graphe des axes partiels

res <- MFA(wine, group=c(2,5,3,10,9,2), type=c("n",rep("s",5)),ncp=3, name.group=c("orig","olf","vis","olfag","gust","ens"),num.group.sup=c(1,6))

22

−4 −2 0 2 4

02

46


Dim 1 (49.38%)

Dim

2 (

19.4

9%)

Saumur

BourgueuilChinon

ReferenceEnv1

Env2

Env4

olfvisolfaggust

!!!!!

plot(res, choix="axes")

23

−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

−1.

0−

0.5

0.0

0.5

1.0

Partial axes

Dim 1 (49.38%)

Dim

2 (

19.4

9%)

Dim1.orig

Dim2.orig

Dim3.origDim1.olf

Dim2.olf

Dim3.olf Dim1.vis

Dim2.vis

Dim3.vis

Dim1.olfag

Dim2.olfag

Dim3.olfag Dim1.gust

Dim2.gust

Dim3.gust

Dim1.ens

Dim2.ens

origolfvisolfaggustens

# Description des dimensions

dimdesc(res)

## $Dim.1## $Dim.1$quanti## correlation p.value## Surface.feeling 0.9501131 4.605897e-11## Aroma.persistency 0.9298582 1.082737e-09## Intensity 0.9241930 2.214222e-09## Aroma.intensity 0.9183490 4.380472e-09## Harmony 0.9024824 2.221510e-08## Visual.intensity 0.8811873 1.331392e-07## Nuance 0.8623373 4.995733e-07## Attack.intensity 0.8439524 1.524322e-06## Aroma.quality.before.shaking 0.8352510 2.462507e-06## Smooth 0.8299677 3.251800e-06## Astringency 0.7966486 1.549124e-05

24

## Quality.of.odour 0.7909364 1.967655e-05## Alcohol 0.7792689 3.137694e-05## Balance 0.7740492 3.832036e-05## Typical 0.7656957 5.221396e-05## Aroma.quality 0.7484543 9.521647e-05## Overall.quality 0.7472814 9.901881e-05## Fruity 0.7333860 1.550774e-04## Fruity.before.shaking 0.7160259 2.618708e-04## Odor.Intensity 0.6270975 2.345881e-03## Odor.Intensity.before.shaking 0.5908036 4.800834e-03## Flower.before.shaking 0.4387181 4.664182e-02## Plante -0.5064137 1.915100e-02#### $Dim.1$category## Estimate p.value## Reference 1.444131 0.01043873###### $Dim.2## $Dim.2$quanti## correlation p.value## Spice.before.shaking 0.8650199 4.189450e-07## Spice 0.6910122 5.233277e-04## Odor.Intensity.before.shaking 0.6672378 9.524504e-04## Bitterness 0.6506434 1.404051e-03## Plante 0.6290859 2.249914e-03## Odor.Intensity 0.5755174 6.336628e-03## Astringency 0.4608480 3.550587e-02## Smooth -0.4372509 4.746573e-02## Typical -0.4655898 3.341665e-02## Overall.quality -0.5036281 1.993378e-02## Balance -0.5249698 1.454356e-02## Aroma.quality -0.5624494 7.951915e-03## Flower -0.5727974 6.648318e-03#### $Dim.2$quali## R2 p.value## Soil 0.8255815 1.127917e-06#### $Dim.2$category## Estimate p.value## Env4 2.566606 2.650535e-07###### $Dim.3## $Dim.3$quanti## correlation p.value## Flower.before.shaking 0.6373128 0.001887133## Flower 0.6364710 0.001921831## Fruity -0.4941180 0.022801235## Fruity.before.shaking -0.5374876 0.011976303

25

Documents

Analyse Factorielle Multiple (AFM) avec FactoMineR sur la